Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1997-11-21
Phys.Rev.D57:4686-4690,1998
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
6 pages RevTeX file with four figures incorporated (uses RevTeX and epsf). Matches published version
Scientific paper
10.1103/PhysRevD.57.4686
We present a phase-plane analysis of cosmologies containing a barotropic fluid with equation of state $p_\gamma = (\gamma-1) \rho_\gamma$, plus a scalar field $\phi$ with an exponential potential $V \propto \exp(-\lambda \kappa \phi)$ where $\kappa^2 = 8\pi G$. In addition to the well-known inflationary solutions for $\lambda^2 < 2$, there exist scaling solutions when $\lambda^2 > 3\gamma$ in which the scalar field energy density tracks that of the barotropic fluid (which for example might be radiation or dust). We show that the scaling solutions are the unique late-time attractors whenever they exist. The fluid-dominated solutions, where $V(\phi)/\rho_\gamma \to 0$ at late times, are always unstable (except for the cosmological constant case $\gamma = 0$). The relative energy density of the fluid and scalar field depends on the steepness of the exponential potential, which is constrained by nucleosynthesis to $\lambda^2 > 20$. We show that standard inflation models are unable to solve this `relic density' problem.
Copeland Edmund J.
Liddle Andrew R.
Wands David
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